## Differential and Integral Equations

### Time-dependent nonlinear evolution equations

Chin-Yuan Lin

#### Abstract

Of concern is the nonlinear evolution equation \begin{align} \frac{du}{dt} & \in A(t)u,\ \ 0 < t < T \notag \\ u(0) & = u_{0} \notag \end{align} in a real Banach space $X$, where $A(t) : D(A(t)) \subset X \longrightarrow X$ is a time-dependent, nonlinear, multivalued operator acting on $X$. It is shown that under certain assumptions on $A(t)$, the equation has a strong solution. Applications to nonlinear parabolic boundary value problems with time-dependent boundary conditions are given.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 3 (2002), 257-270.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060860

Mathematical Reviews number (MathSciNet)
MR1870643

Zentralblatt MATH identifier
1041.34049

Subjects
Primary: 34G25: Evolution inclusions
Secondary: 47N20: Applications to differential and integral equations

#### Citation

Lin, Chin-Yuan. Time-dependent nonlinear evolution equations. Differential Integral Equations 15 (2002), no. 3, 257--270. https://projecteuclid.org/euclid.die/1356060860